About 6.4 million women become pregnant in the U.S. each year, and about 70% of those women have maternal serum screening and/or an ultrasound test in an attempt to determine risks for common birth defects, such as those resulting from trisomy 13, 18, and 21 (Down Syndrome). Both the sensitivity and specificity of these common non-invasive screening tools are extremely poor. The best current non-invasive tests lead to a false positive rate between 7 and 20%. This high false positive rate has two catastrophic consequences for American families and society. First, it creates a large market for the two invasive diagnostic tests, chorionic villus sampling (CVS) and amniocentesis, which each carry a fetal loss rate of 0.5%-1%. These invasive tests directly result in the loss of thousands of normal fetuses annually. Second, the high false positive rate heightens maternal anxiety and stress in the large and fixed proportion of pregnant American women who receive false positive results. However, prenatal diagnosis are critical in managing a pregnancy with chromosomal abnormalities and localized genetic abnormalities, as the diagnosis can allow for interventional care during delivery and can prevent devastating consequences for the neonate. Non-invasive tests that rely on detection of short tandem repeat (STR) sequences and low complexity regions have low-sensitivity and are often riddled with false-positives and false-negatives. STR sequences and low complexity regions are highly susceptible to polymerase-induced stutters and therefore generate significant PCR-induced noise. This high background noise makes the detection and accurate quantification of low concentrations of fetal DNA in maternal plasma very unlikely, making these poor markers for use in non-invasive tests for fetal chromosomal abnormalities. Thus there is a tremendous need for the development of a sensitive and specific non-invasive test for chromosomal abnormalities, e.g., for prenatal diagnostics.